Program to calculate the value of sin(x) and cos(x) using Expansion

Difficulty Level : Medium
Last Updated : 03 Oct, 2019

Given a value of angle, you need to calculate Sin and Cos values corresponding to it.

For sin function

Examples:

Input : 90
Output : 1

$Sin(x)=\sum_{k=0}^{\infty } \frac {(-1)^k}{(2k+1)!}x^{2k+1}=x-\frac {x^3}{3!} + \frac {x^5}{5!} - .........$

C++

// CPP code for implementing sin function 
#include <iostream> 
#include <math.h> 
using namespace std; 
  
// Function for calculating sin value 
void cal_sin(float n) 
{     
    float accuracy = 0.0001, denominator, sinx, sinval; 
      
    // Converting degrees to radian 
    n = n * (3.142 / 180.0);  
  
    float x1 = n; 
      
    // maps the sum along the series 
    sinx = n;          
      
    // holds the actual value of sin(n) 
    sinval = sin(n);     
    int i = 1; 
    do
    { 
        denominator = 2 * i * (2 * i + 1); 
        x1 = -x1 * n * n / denominator; 
        sinx = sinx + x1; 
        i = i + 1; 
    } while (accuracy <= fabs(sinval - sinx)); 
    cout << sinx; 
} 
  
// Main function 
int main() 
{ 
    float n = 90; 
    cal_sin(n); 
    return 0; 
} 

Java

import static java.lang.Math.sin; 
  
// JAVA code for implementing sin function 
  
class GFG { 
  
// Function for calculating sin value  
static void cal_sin(float n)  
{      
    float accuracy = (float) 0.0001, denominator, sinx, sinval;  
      
    // Converting degrees to radian  
    n = n * (float)(3.142 / 180.0);  
  
    float x1 = n;  
      
    // maps the sum along the series  
    sinx = n;          
      
    // holds the actual value of sin(n)  
    sinval = (float)sin(n);      
    int i = 1;  
    do
    {  
        denominator = 2 * i * (2 * i + 1);  
        x1 = -x1 * n * n / denominator;  
        sinx = sinx + x1;  
        i = i + 1;  
    } while (accuracy <= sinval - sinx);  
       System.out.println(sinx);  
}  
  
// Main function  
  
  
    public static void main(String[] args) { 
        float n = 90;  
    cal_sin(n);  
      
    } 
} 

Python3

# Python3 code for implementing  
# sin function 
import math; 
  
# Function for calculating sin value 
def cal_sin(n): 
  
    accuracy = 0.0001; 
      
    # Converting degrees to radian 
    n = n * (3.142 / 180.0);  
      
    x1 = n; 
      
    # maps the sum along the series 
    sinx = n;      
      
    # holds the actual value of sin(n) 
    sinval = math.sin(n);  
    i = 1; 
    while(True): 
      
        denominator = 2 * i * (2 * i + 1); 
        x1 = -x1 * n * n / denominator; 
        sinx = sinx + x1; 
        i = i + 1; 
        if(accuracy <= abs(sinval - sinx)): 
            break; 
          
    print(round(sinx)); 
  
# Driver Code 
n = 90; 
cal_sin(n); 
      
# This code is contributed by mits 

C#

// C# code for implementing sin function  
using System; 
  
class GFG 
{ 
// Function for calculating sin value  
static void cal_sin(float n)  
{  
    float accuracy = (float) 0.0001,  
                      denominator, sinx, sinval;  
      
    // Converting degrees to radian  
    n = n * (float)(3.142 / 180.0);  
  
    float x1 = n;  
      
    // maps the sum along the series  
    sinx = n;      
      
    // holds the actual value of sin(n)  
    sinval = (float)Math.Sin(n);      
    int i = 1;  
    do
    {  
        denominator = 2 * i * (2 * i + 1);  
        x1 = -x1 * n * n / denominator;  
        sinx = sinx + x1;  
        i = i + 1;  
    } while (accuracy <= sinval - sinx);  
      
    Console.WriteLine(sinx);  
}  
  
// Driver Code 
static public void Main () 
{ 
    float n = 90;  
    cal_sin(n);  
} 
} 
  
// This code is contributed by jit_t 

PHP

<?php 
// PHP code for implementing sin function 
  
// Function for calculating sin value 
function cal_sin($n) 
{  
    $accuracy = 0.0001; 
      
    // Converting degrees to radian 
    $n = $n * (3.142 / 180.0);  
  
    $x1 = $n; 
      
    // maps the sum along the series 
    $sinx = $n;          
      
    // holds the actual value of sin(n) 
    $sinval = sin($n);  
    $i = 1; 
    do
    { 
        $denominator = 2 * $i * (2 * $i + 1); 
        $x1 = -$x1 * $n * $n / $denominator; 
        $sinx = $sinx + $x1; 
        $i = $i + 1; 
    } while ($accuracy <= abs($sinval - $sinx)); 
    echo round($sinx); 
} 
  
// Main function 
  
    $n = 90; 
    cal_sin($n); 
      
// This code is contributed by mits 
?> 

Output:

For cos function

Examples:

Input : 30
Output : 0.86602

$Cos(x)=\sum_{k=0}^{\infty } \frac {(-1)^k}{(2k)!}x^{2k}=1-\frac {x^2}{2!} + \frac {x^4}{4!} -.....$

C++

// CPP code for implementing cos function 
#include <iostream> 
#include <math.h> 
using namespace std; 
  
// Function for calculation 
void cal_cos(float n) 
{ 
    float accuracy = 0.0001, x1, denominator, cosx, cosval; 
      
    // Converting degrees to radian 
    n = n * (3.142 / 180.0); 
      
    x1 = 1; 
      
    // maps the sum along the series 
    cosx = x1;          
      
    // holds the actual value of sin(n) 
    cosval = cos(n); 
    int i = 1; 
    do
    { 
        denominator = 2 * i * (2 * i - 1); 
        x1 = -x1 * n * n / denominator; 
        cosx = cosx + x1; 
        i = i + 1; 
    } while (accuracy <= fabs(cosval - cosx)); 
    cout << cosx; 
} 
  
// Main function 
int main() 
{ 
    float n = 30; 
    cal_cos(n); 
}  

Java

// Java code for implementing cos function 
  
import static java.lang.Math.cos; 
  
class GFG { 
// Function for calculation 
  
static void cal_cos(float n) { 
    float accuracy = (float) 0.0001, x1, denominator, cosx, cosval; 
    // Converting degrees to radian 
    n = n * (float) (3.142 / 180.0); 
    x1 = 1; 
    // maps the sum along the series 
    cosx = x1; 
    // holds the actual value of sin(n) 
    cosval = (float) cos(n); 
    int i = 1; 
    do { 
        denominator = 2 * i * (2 * i - 1); 
        x1 = -x1 * n * n / denominator; 
        cosx = cosx + x1; 
        i = i + 1; 
          
    } 
    while (accuracy <= cosval - cosx); 
    System.out.println(cosx); 
      
} 
  
// Main function 
public static void main(String[] args) { 
    float n = 30; 
    cal_cos(n); 
      
} 
} 

Python3

# Python 3 code for implementing cos function 
  
from math import fabs, cos 
  
# Function for calculation 
def cal_cos(n): 
    accuracy = 0.0001
  
    # Converting degrees to radian 
    n = n * (3.142 / 180.0) 
      
    x1 = 1
      
    # maps the sum along the series 
    cosx = x1 
      
    # holds the actual value of sin(n) 
    cosval = cos(n) 
    i = 1
  
    denominator = 2 * i * (2 * i - 1) 
    x1 = -x1 * n * n / denominator 
    cosx = cosx + x1 
    i = i + 1
    while (accuracy <= fabs(cosval - cosx)): 
        denominator = 2 * i * (2 * i - 1) 
        x1 = -x1 * n * n / denominator 
        cosx = cosx + x1 
        i = i + 1
  
    print('{0:.6}'.format(cosx)) 
  
# Driver Code 
if __name__ == '__main__': 
    n = 30
    cal_cos(n) 
  
# This code is contributed by 
# Sahil_Shelangia 

C#

// C# code for implementing cos function  
  
using System; 
class GFG {  
// Function for calculation  
  
static void cal_cos(float n) {  
    float accuracy = (float) 0.0001, x1, denominator, cosx, cosval;  
    // Converting degrees to radian  
    n = n * (float) (3.142 / 180.0);  
    x1 = 1;  
    // maps the sum along the series  
    cosx = x1;  
    // holds the actual value of sin(n)  
    cosval = (float) Math.Cos(n);  
    int i = 1;  
    do {  
        denominator = 2 * i * (2 * i - 1);  
        x1 = -x1 * n * n / denominator;  
        cosx = cosx + x1;  
        i = i + 1;  
          
    }  
    while (accuracy <= cosval - cosx);  
    Console.WriteLine(cosx);  
      
}  
  
// Main function  
static void Main() {  
    float n = 30;  
    cal_cos(n);  
      
}  
}  
// This code is contributed by mits 

PHP

<?php 
// PHP code for implementing cos function 
  
// Function for calculation 
function cal_cos($n) 
{ 
    $accuracy = 0.0001; 
      
    // Converting degrees to radian 
    $n = $n * (3.142 / 180.0); 
      
    $x1 = 1; 
      
    // maps the sum along the series 
    $cosx = $x1;          
      
    // holds the actual value of sin(n) 
    $cosval = cos($n); 
    $i = 1; 
    do
    { 
        $denominator = 2 * $i * (2 * $i - 1); 
        $x1 = -$x1 * $n * $n / $denominator; 
        $cosx = $cosx + $x1; 
        $i = $i + 1; 
    } while ($accuracy <= abs($cosval - $cosx)); 
    echo round($cosx, 6); 
} 
  
// Driver Code 
$n = 30; 
cal_cos($n); 
  
// This code is contributed by mits 
?> 

Output:

0.86602

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